A085062 a(n) = A085060(n)/9 - 1/3.

0, 1, 1, 4, 2, 4, 3, 13, 4, 7, 5, 13, 6, 10, 7, 40, 8, 13, 9, 22, 10, 16, 11, 40, 12, 19, 13, 31, 14, 22, 15, 121, 16, 25, 17, 40, 18, 28, 19, 67, 20, 31, 21, 49, 22, 34, 23, 121, 24, 37, 25, 58, 26, 40, 27, 94, 28, 43, 29, 67, 30, 46, 31, 364, 32, 49, 33, 76, 34, 52, 35, 121, 36, 55

Offset

0,4

Comments

Interlacing of A001477 and A085060 / 3. - Ruud H.G. van Tol, Aug 30 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

J. C. Lagarias and N. J. A. Sloane, Approximate Squaring, Experimental Math., 13 (2004), 113-128; alternative link; pdf, ps.

Formula

a(n) mod 2 = A292077(n+1). - Alois P. Heinz, Jul 01 2023

a(2*n) = n; a(2*n+1) = 3 * a(n) + 1. - Ruud H.G. van Tol, Aug 31 2024

Sum_{k=1..n} a(k) ~ n^2/2. - Amiram Eldar, Apr 04 2026

Maple

a:= n-> `if`(n::odd, a((3*n+1)/2), n/2):
seq(a(n), n=0..100);  # Alois P. Heinz, Jul 01 2023

Mathematica

a[n_] := ((3/2)^IntegerExponent[n+1, 2]*(n+1) - 1)/2; Array[a, 100, 0] (* Amiram Eldar, Apr 04 2026 *)

Prog

(PARI) a(n) = ((3/2)^valuation(n++, 2)*n-1)/2; \\ Ruud H.G. van Tol, Aug 30 2024
(Python)
def A085062(n): return ((k:=n+1)*3**((m:=(-k&k).bit_length())-1)>>m) # Chai Wah Wu, Feb 26 2025

Crossrefs

Cf. A085060, A292077.

Bisection gives: A001477 (even part).

Sequence in context: A010316 A083954 A038702 * A053051 A075234 A232715

Adjacent sequences: A085059 A085060 A085061 * A085063 A085064 A085065

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 11 2003

Status

approved